From the 4th picture of that Amazon item, I would use either 3C or 2.4D tip, add solder to it so it so it'll have contact with the solder of the capacitor pin. An important point to consider is a power of the solder iron - according to the description, it's 60W so should be enough for that kind of board.
I must admit, however, the iron does look somewhat tiny for the advertised 60W - for me it looks more like a 10-15 real watt iron (for visual comparison, look at Hakko 70w station), but who knows, maybe they are making them more efficient these days. In the past, I had difficulties unsoldering caps from an Asus graphics card (multi-layer PCB with a lot of copper) with a 120W Weller station and largest tip, but in contrast, I've never had issues melting solder in old motherboards using my 50W station that I got from SparkFun years ago.
Also, for cleaning iron tip, I'd suggest getting coiled brass. When working, the tip should appear as shiny metal, not black or gray.